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Proof step 17 from proof downcase-C (previous step)

pos('A', sortedchars) ≤ 30, 30 ≤ pos('Z', sortedchars), pos('A', sortedchars) ≤ pos('Z', sortedchars) ⊦ s→l(sortedchars)[30 + (58 - pos('A', sortedchars))] = 'c', pos('Z', sortedchars) = 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 18:
58 = n0 + pos('A', sortedchars) ∧ pos('A', sortedchars) ≤ 58, pos('A', sortedchars) ≤ 30, 30 ≤ pos('Z', sortedchars), pos('A', sortedchars) ≤ pos('Z', sortedchars) ⊦ s→l(sortedchars)[30 + n0] = 'c', pos('Z', sortedchars) = 0

Rule argument

spec: nat inst: name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [58, pos('A', sortedchars), n] flags:

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ m < n → n ≠ 0; (forward)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: 58, pos('A', sortedchars), n